Is there a word for the phenomenon where people have extreme emotional distress towards others who ask for evidence or question the validity of a popularly accepted claim, where the distress commonly accompanies condemnation and/or threats of exile to the individual questioning the claim?

For example, assume most people in the world believe a teapot orbits the Sun between the Earth and Mars. A guy comes along and says, I don’t believe that, could you show me the evidence of that? The crowd gets angry and condemns the man. They ask him to back up his claim or he will be exiled forever. Of course he cannot back up his claim, it's much like proving Santa Claus doesn’t exist. So, he is destined to be hated, since they cannot prove their original claim.

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Dogmatism and skepticism are both, in a sense, absolute philosophies; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or ignorance.
- Bertrand Russell

Dogmatism is also characterized by three emotional characteristics: Association between beliefs and anxiety or fear, association between beliefs and anger, as well as existential despair (see Johnson, 2009). First, discussions or reflections about their beliefs can elicit anxiety or fear. If their beliefs are challenged or questioned, they often seem especially agitated and uneasy. Consequently, they often avoid contexts in which their beliefs might be queried. Hence, dogmatism seems to represent an attempt to foster certainty and to curb anxiety.

How about knee-jerk reactionaries? Something about the thoughtless reaction to the skeptic's question brought this phrase to mind. Of course, this isn't a word for the phenomenon, it is a phrase that describes the people who exhibit the phenomenon.

The people who do the hating of the one who questions them are engaged in confirmation bias, so I think you could say they are biased. They don't want to hear anything that might put their beliefs into question. Wikipedia has a good article on confirmation bias. Here is an excerpt:

"Confirmation bias (also called confirmatory bias or myside bias) is a tendency of people to favor information that confirms their beliefs or hypotheses. People display this bias when they gather or remember information selectively, or when they interpret it in a biased way. The effect is stronger for emotionally charged issues and for deeply entrenched beliefs. For example, in reading about gun control, people usually prefer sources that affirm their existing attitudes. They also tend to interpret ambiguous evidence as supporting their existing position. Biased search, interpretation and memory have been invoked to explain attitude polarization (when a disagreement becomes more extreme even though the different parties are exposed to the same evidence), belief perseverance (when beliefs persist after the evidence for them is shown to be false), the irrational primacy effect (a greater reliance on information encountered early in a series) and illusory correlation (when people falsely perceive an association between two events or situations)."

And there is attitude or belief polarization, which stems from confirmation bias. You could say that the people who hate skeptics are polarized. Attitude polarization:

"is a phenomenon in which a disagreement becomes more extreme as the different parties consider evidence on the issue. It is one of the effects of confirmation bias: the tendency of people to search for and interpret evidence selectively, to reinforce their current beliefs or attitudes. When people encounter ambiguous evidence, this bias can potentially result in each of them interpreting it as in support of their existing attitudes, widening rather than narrowing the disagreement between them."

And there is an extreme form of confirmation bias called denialism; those who practice it are termed denialists.

"In science, denialism has been defined as the rejection of basic concepts that are undisputed and well-supported parts of the scientific consensus on a topic in favor of ideas that are both radical and controversial. It has been proposed that the various forms of denialism have the common feature of the rejection of overwhelming evidence and the generation of a controversy through attempts to deny that a consensus exists."